Reflectionless Sturm-Liouville equations

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, we also provide the proofs of several basic estimates, e.g., bounds and asymptotics for the relevant m-functions.

Original languageEnglish (US)
Pages (from-to)207-225
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume208
Issue number1 SPEC. ISS.
DOIs
StatePublished - Nov 1 2007
Externally publishedYes

Keywords

  • Scattering coefficients
  • Sturm-Liouville equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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